Generative Distributionally Robust Optimization

2026-07-27

AI Summary

Existing distributionally robust optimization (DRO) methods struggle to simultaneously support arbitrary conditional generators and guarantee that the worst-case distribution lies within a specified generator family when only sample access is available. This work proposes the GDRO framework, which introduces a sampler–Sinkhorn pairing mechanism that treats a sample-accessible conditional generator as the nominal model and leverages Sinkhorn divergence to quantify distributional discrepancies—enabling likelihood-free DRO. By integrating dual differentiable optimization with finite-sample approximation, GDRO achieves substantial improvements over nominal policies: it reduces regret in rare-event inventory scenarios by 60% with explicit generators and cuts collision rates by 50% in SocialGAN-based navigation with implicit generators.

Abstract

Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.

Problem

• Distributionally Robust Optimization
• Generative Models
• Adversarial Distribution
• Sample-based Estimation
• Conditional Generators

Innovation

• Generative Distributionally Robust Optimization
• conditional generator
• Sinkhorn divergence
• sample-based estimation
• primal-dual implementation